Inference of internal stress in a cell monolayer

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy (BISM), is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply BISM to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi-one-dimensional geometry.Comment: 38 pages, 14 figure

A migrating epithelial monolayer flows like a Maxwell viscoelastic liquid

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby Canine Kidney (MDCK) epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbour rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behaviour (and not with a Kelvin-Voigt viscoelastic solid behaviour). The value of the associated relaxation time is measured as $\tau = 70 \pm 15$~min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration.Comment: 17 pages, 15 figure

Polymers in linear shear flow: a numerical study

We study the dynamics of a single polymer subject to thermal fluctuations in a linear shear flow. The polymer is modeled as a finitely extendable nonlinear elastic FENE dumbbell. Both orientation and elongation dynamics are investigated numerically as a function of the shear strength, by means of a new efficient integration algorithm. The results are in agreement with recent experiments.Comment: 7 pages, see also the preceding paper (http://arxiv.org/nlin.CD/0503028

Tension Dynamics and Linear Viscoelastic Behavior of a Single Semiflexible Polymer Chain

We study the dynamical response of a single semiflexible polymer chain based on the theory developed by Hallatschek et al. for the wormlike-chain model. The linear viscoelastic response under oscillatory forces acting at the two chain ends is derived analytically as a function of the oscillation frequency . We shall show that the real part of the complex compliance in the low frequency limit is consistent with the static result of Marko and Siggia whereas the imaginary part exhibits the power-law dependence +1/2. On the other hand, these compliances decrease as the power law -7/8 for the high frequency limit. These are different from those of the Rouse dynamics. A scaling argument is developed to understand these novel results.Comment: 23 pages, 6 figure

Active forces modulate collective behaviour and cellular organization

Biological tissues are composed of various cell types working cooperatively to perform their respective function within organs and the whole body. During development, embryogenesis followed by histogenesis relies on orchestrated division, death, differentiation and collective movements of cellular constituents. These cells are anchored to each other and/or the underlying substrate through adhesion complexes and they regulate force generation by active cytoskeleton remodeling. The resulting changes in contractility at the level of each single cell impact tissue architecture and remodeling by triggering changes in cell shape, cell movement and remodeling of the surrounding environment. These out of equilibrium processes occur through cellular energy consumption, allowing biological systems to be described by active matter physics. Cytoskeleton filaments, bacterial and eukaryotic cells can be considered as a sub-class of active matter termed "active nematics". These biological objects can be modelled as rod-like elements to which nematic liquid crystal theories can be applied. In this work, using an analogy from liquid crystal physics, we show that cell sorting and boundary formation can be explained using differences in nematic activity. This difference in nematic activity arises from a balance of inter-and intra-cellular activity

Deposited footprints let cells switch between confined, oscillatory, and exploratory migration

For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion

Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Collective migration of an epithelial monolayer in response to a model wound

Using an original microfabrication-based technique, we experimentally study situations in which a virgin surface is presented to a confluent epithelium with no damage made to the cells. Although inspired by wound-healing experiments, the situation is markedly different from classical scratch wounding because it focuses on the influence of the free surface and uncouples it from the other possible contributions such as cell damage and/or permeabilization. Dealing with Madin-Darby canine kidney cells on various surfaces, we found that a sudden release of the available surface is sufficient to trigger collective motility. This migration is independent of the proliferation of the cells that mainly takes place on the fraction of the surface initially covered. We find that this motility is characterized by a duality between collective and individual behaviors. On the one hand, the velocity fields within the monolayer are very long range and involve many cells in a coordinated way. On the other hand, we have identified very active "leader cells" that precede a small cohort and destabilize the border by a fingering instability. The sides of the fingers reveal a pluricellular actin "belt" that may be at the origin of a mechanical signaling between the leader and the followers. Experiments performed with autocrine cells constitutively expressing hepatocyte growth factor (HGF) or in the presence of exogenous HGF show a higher average velocity of the border and no leader

Local contractions regulate E-cadherin rigidity sensing

E-cadherin is a major cell-cell adhesion molecule involved in mechanotransduction at cell-cell contacts in tissues. Because epithelial cells respond to rigidity and tension in tissue through E-cadherin, there must be active processes that test and respond to the mechanical properties of these adhesive contacts. Using submicrometer, E-cadherincoated polydimethylsiloxane pillars, we find that cells generate local contractions between E-cadherin adhesions and pull to a constant distance for a constant duration, irrespective of pillar rigidity. These cadherin contractions require nonmuscle myosin IIB, tropomyosin 2.1, alpha-catenin, and binding of vinculin to.-catenin. Cells spread to different areas on soft and rigid surfaces with contractions, but spread equally on soft and rigid without. We further observe that cadherin contractions enable cells to test myosin IIA-mediated tension of neighboring cells and sort out myosin IIA-depleted cells. Thus, we suggest that epithelial cells test and respond to the mechanical characteristics of neighboring cells through cadherin contractions